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The distance at which an object falls varies as the square of the time of falling. A rock dropped from a window 35 feet 1 inch hits the ground in 1. 5 seconds. A rock dropped from a bridge hits the water in 4.5 seconds. Calculate height of bridge. Thanks.

"The distance at which an object falls varies as the square of the time of falling."

That means the equation relating distance and time has the form

d = kt˛

where d and t are the distance and time, respectively, and k is a constant.

"A rock dropped from a window 35 feet 1 inch hits the ground in 1. 5 seconds."

t = 1.5 sec

d = 35 feet 1 inch = (35 + 1/12) feet = 421/12 feet

Use the first equation to determine k:

421/12 = k(1.5˛)

k = (421/27) feet per second˛

"A rock dropped from a bridge hits the water in 4.5 seconds."

d = (421/27)(4.5˛) = 315.75

The height of the bridge is 315.75 feet.

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